source: ncert
topic: algebra
class_level: class_8
chapter: ch2
difficulty: beginner
Class 8 | Ch2: Linear Equations in One Variable Linear equation: variable has power 1 only. ax+b=c form. Can involve fractions and variables on both sides. SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES: Collect variable terms on one side, constants on other. 3x+2=5x-4 → 2+4=5x-3x → 6=2x → x=3. SOLVING EQUATIONS WITH FRACTIONS: Multiply both sides by LCM of all denominators to clear fractions. (2x+3)/5-(x-4)/3=2. LCM=15. Multiply: 3(2x+3)-5(x-4)=30. 6x+9-5x+20=30 → x+29=30 → x=1. WORD PROBLEMS - STANDARD TYPES: Age problems: Let present age=x. Set up equation from given conditions. Number problems: Let number=x. Translate words to equation. Geometry problems: Use perimeter/area formulas. Money/mixture problems: Set up equation for totals. SOLVED EXAMPLES: Example 1: (2x+3)/5-(x-4)/3=2 Multiply by 15: 3(2x+3)-5(x-4)=30 → 6x+9-5x+20=30 → x=1. Verify: (2+3)/5-(1-4)/3=1+1=2. Correct. Example 2: A number is 4 more than twice another. Sum=40. Let numbers be x and 2x+4. x+(2x+4)=40 → 3x=36 → x=12. Numbers: 12 and 28. Verify: 12+28=40 and 28=2(12)+4. Correct. Example 3: Present age ratio of A and B is 3:4. After 5 years ratio becomes 4:5. Find ages. Let ages: 3x and 4x. (3x+5)/(4x+5)=4/5 → 15x+25=16x+20 → x=5. Ages: 15 and 20. COMMON MISTAKES: When multiplying by LCM, multiply EVERY term including constants. Verify answer by substituting back in ORIGINAL equation.